Model-Based Clustering Methods for Time Series

Abstract

This paper considers the problem of clustering n observed time series $\mathbf{x}_{k} =\{\ x_{k}(t)\ \vert \ t \in \mathcal{T}\}$, k = 1, …, n, with time points t in a suitable time range $\mathcal{T}$, into a suitable number m of clusters $C_{1},\ldots,C_{m} \subset \{ 1,\ldots,n\}$ each one comprising time series with a ‘similar’ structure. Classical approaches might typically proceed by first computing a dissimilarity matrix and then applying a traditional, possibly hierarchical clustering method. In contrast, here we will present a brief survey about various approaches that start by defining probabilistic clustering models for the time series, i.e., with class-specific distribution models, and then determine a suitable (hopefully optimum) clustering by statistical tools like maximum likelihood and optimization algorithms. In particular, we will consider models with class-specific Gaussian processes and Markov chains.